code: def _ode_lie_group(s, func, order, match):
      heuristics = lie_heuristics
      inf = {}
      f = func.func
      x = func.args[0]
      df = func.diff(x)
      xi = Function("xi")
      eta = Function("eta")
      xis = match["xi"]
      etas = match["eta"]
      y = match.pop("y", None)
      if y:
          h = -simplify(match[match["d"]] / match[match["e"]])
          y = y
      else:
          y = Dummy("y")
          h = s.subs(func, y)
  
      if xis is not None and etas is not None:
          inf = [{xi(x, f(x)): S(xis), eta(x, f(x)): S(etas)}]
  
          if checkinfsol(Eq(df, s), inf, func=f(x), order=1)[0][0]:
              heuristics = ["user_defined"] + list(heuristics)
  
      match = {"h": h, "y": y}
  
      # This is done so that if any heuristic raises a ValueError
      # another heuristic can be used.
      sol = None
      for heuristic in heuristics:
          sol = _ode_lie_group_try_heuristic(
              Eq(df, s), heuristic, func, match, inf
          )
          if sol:
              return sol
      return sol
  
imports: from itertools import islice
  from sympy.core import Add, S, Mul, Pow
  from sympy.core.exprtools import factor_terms
  from sympy.core.function import Function, AppliedUndef, expand
  from sympy.core.relational import Equality, Eq
  from sympy.core.symbol import Symbol, Wild, Dummy, symbols
  from sympy.functions import exp, log
  from sympy.integrals.integrals import integrate
  from sympy.polys import Poly
  from sympy.polys.polytools import cancel, div
  from sympy.simplify import collect, powsimp, separatevars, simplify
  from sympy.solvers import solve
  from sympy.solvers.pde import pdsolve
  from sympy.utilities import numbered_symbols
  from sympy.solvers.deutils import _preprocess, ode_order
  from .ode import checkinfsol
label_desc: Use image node_id 2 for calling a global function with example usage: _ode_lie_group(s, func, order, match) and returns: sol, sol